WASHINGTON -- Last week former President Ronald Reagan surprised the Republican Party with his endorsement of a bill requiring a waiting period for the purchase of handguns. This week, after the Senate Democratic leader expressed his opposition to the measure, it was the Democrats' turn.

Before Mr. Reagan's announcement, the bill faced tough going in the House, where its opponents included the Bush administration aswell as the National Rifle Association. But advocates of gun control believed that his endorsement last Thursday would help the measure, which is named after James S. Brady, Mr. Reagan's press secretary, who was left disabled by an assassin's bullet in 1981.

Then, on Sunday, the Senate majority leader, George J. Mitchell of Maine, said on the NBC News program "Meet the Press" that he did not support the bill and, moreover, did not "know of any member of Congress who has changed his mind because President Reagan has changed his mind."

The senator said he was not against the concept of a waiting period but wanted to include a national registry that would allow the police in one state to conduct background checks across state lines.

Supporters of the bill said that it would take years to set up such a system and expressed surprise and anger over Mr. Mitchell's comments.

"I was pretty much aghast at what he said," said Representative Lawrence J. Smith, D-Fla., who is asponsor of the bill. "I think that most of the country favors a waiting period."

Representative John Conyers Jr., D-Mich., who is also a sponsor, said: "I am amazed that Mitchell found something to quarrel with about a measure of this simplicity. I don't know what his problem is in connection with a seven-day waiting period."

Supporters of the bill contrasted Mr. Mitchell's position with that of Speaker Thomas S. Foley, D-Wash., who is also cool to gun-control laws.Mr. Foley has so far declined to express his views on the bill.

The Senate Republican leader, Bob Dole of Kansas, also opposes the bill but takes a somewhat different position from Mr. Mitchell's. He prefers a nationwide computerized system, or hot line, that would let gun dealers conduct instant background checks.

The Republican leader in the House, Representative Robert H. Michel of Illinois, could not be reached for comment on the bill.

Mr. Mitchell's support for the billis considered crucial. Supporters believe that they will be able to pass the bill in the House, but they note that last May the Senate approved by a single vote a measure that would ban the sale and manufacture of nine types of semiautomatic weapons. Mr. Mitchell threw his support behind that bill at the last minute. The House never voted on the ban.

"There's no question it's going to be more difficult with George Mitchell against it," said Representative William J. Hughes, D-N.J., who supports the Brady bill.